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Rate conservation for stationary processes

Published online by Cambridge University Press:  14 July 2016

Josep M. Ferrandiz  and
Aurel A. Lazar
Josep M. Ferrandiz
Affiliation:
Columbia University
Aurel A. Lazar*
Affiliation:
Columbia University
*
∗∗Postal address: Department of Electrical Engineering, 1312 S. W. Mudd Building, Columbia University, New York, NY 10027, USA.
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Abstract

We derive a rate conservation law for distribution densities which extends a result of Brill and Posner. Based on this conservation law, we obtain a generalized Takács equation for the G/G/m/B queueing system that only requires the existence of a stochastic intensity for the arrival process and the residual service time distribution density for the G/GI/1/B queue. Finally, we solve Takács' equation for the N/GI/1/∞ queueing system.

Keywords

PALM PROBABILITYSTOCHASTIC INTENSITYTAKÁCS FORMULAGROUP ARRIVALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 146 - 158
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

∗

Present address: Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS12 6QZ, UK.

References

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